The dog is a yes-animal, very popular with people who can't afford to keep a yes-man.

Davies wryly reframes the sentimental idea of canine loyalty as a kind of inexpensive social validation. A “yes-animal” is valued not for independent judgment but for dependable affirmation—tail-wagging agreement that flatters the owner’s ego and offers uncomplicated companionship. By contrasting the dog with a “yes-man,” Davies points to a broader human desire to be confirmed and admired, whether through paid subordinates or through pets. The joke carries a mild sting: it suggests that some affection for dogs can be less about the animal’s nature than about the owner’s appetite for approval and control, purchased cheaply and without contradiction.